In industrial fields associated with a semiconductor device, a flat panel display, a nano-bio, a nano-imprint, thin film optics, and the like, that have been rapidly developed, importance of a technology capable of non-destructively and contactlessly measuring and evaluating physical properties such as a thicknesses of a thin film of nano samples, a shape of a nano pattern, and the like, in a manufacturing process step has gradually increased.
In accordance with the continuously development of these industrial fields, the thickness of the thin film has been gradually decreased to arrive at a level of several atom layers, and the shape of the nano pattern has become complicated from an existing two-dimensional structure to a three-dimensional structure.
Therefore, in an ellipsometric technology field used as a measuring equipment for a process in these industrial fields, a Mueller-matrix ellipsometer has been developed and used in order to more accurately measure the complicated shape or the complicated physical feature of the sample as described above.
The most widely used Mueller-matrix ellipsometer among Mueller-matrix ellipsometers according to a first exemplary embodiment is an optical element rotation type Mueller-matrix ellipsometer as shown in FIG. 1. The optical element rotation type Mueller-matrix ellipsometer as shown in FIG. 1 is well known as a nano measuring apparatus in which incident light 10 is parallel light generated from a light source 11, and is modified into a specific polarization state by a polarization modifying unit 12 and is then irradiated to a sample 20 to become reflected light (or transmitted light) 30 of which a polarization state is changed by reflection (or transmission) by the sample 20, the change in the polarization state of the reflected light (or the transmitted light) 30 by the sample is measured with respect to any wavelength and incident angle using a polarization analyzing unit 31 and a photo-detector 32, and the measured data are analyzed to find physical property and shape information of the sample.
A core configuration of the optical element rotation type Mueller-matrix ellipsometer will be described. The light source 11, and the polarization modifying unit 12, which is an optical system allowing the light emitted from the light source 11 to be in a specific polarization state, are disposed on a line of the incident light 10, and the polarization analyzing unit 31, which is an optical system analyzing the polarization state of the reflected light (or the transmitted light) and the photo-detector 32 measuring an amount of light passing through the polarization analyzing unit 31 as an electrical signal such as a voltage or a current are disposed on a line of the reflected light (or the transmitted light) 30.
The most widely used Mueller-matrix ellipsometer among various kinds of Mueller-matrix ellipsometers according to the related art is a dual optical element rotation type ellipsometer in which two optical elements rotate at a constant velocity in a predetermined speed ratio. A typical example of the dual optical element rotation type ellipsometer includes a rotating-polarizer rotating-analyzer ellipsometer as shown in FIG. 2, a rotating-compensator rotating-analyzer ellipsometer as shown in FIG. 3, a rotating-polarizer rotating-compensator ellipsometer as shown in FIG. 4, and a dual-rotating-compensator ellipsometer as shown in FIG. 5.
A core component of the rotating-polarizer rotating-analyzer ellipsometer according to a second exemplary embodiment is that the polarization modifying unit 12 is configured of a linear polarizer (commonly called a polarizer 13) rotating at a constant velocity and the polarization analyzing unit 31 is configured of a linear polarizer (commonly called analyzer 33) rotating at a constant velocity in a predetermined ratio different from that of the polarizer 13, as shown in FIG. 2.
A core component of the rotating-compensator rotating-analyzer ellipsometer according to a third exemplary embodiment is that the polarization modifying unit 12 is configured of the polarizer 13 stopping at a designated azimuth angle and a first compensator 14 rotating at a constant velocity and the polarization analyzing unit 31 is configured of an analyzer 33 rotating at a constant velocity in a predetermined ratio different from that of the first compensator 14, as shown in FIG. 3.
A core component of the rotating-polarizer rotating-compensator ellipsometer according to a fourth exemplary embodiment is that the polarization modifying unit 12 is configured of the polarizer 13 rotating at a constant velocity and the polarization analyzing unit 31 is configured of a second compensator 34 rotating at a constant velocity in a predetermined ratio different from that of the polarizer 13 and the analyzer 33 stopping at a designated azimuth angle, as shown in FIG. 4.
A core component of the dual-rotating-compensator ellipsometer according to a fifth exemplary embodiment is that the polarization modifying unit 12 is configured of the polarizer 13 stopping at a designated azimuth angle and the first compensator 14 rotating at a constant velocity and the polarization analyzing unit 31 is configured of the second compensator 34 rotating at a constant velocity in a predetermined ratio different from that of the first compensator 14 and the analyzer 33 stopping at a designated azimuth angle, as shown in FIG. 5.
In these dual optical element rotation type ellipsometer, a Fourier coefficient analyzing method is used in order to analyze a waveform of light intensity when the light intensity periodically changed depending on a time t by rotation of optical elements is measured using a photo-detector in real time.
In the case in which it is assumed that an error is not present in this measuring apparatus, light intensity Iex (t) measured as an electrical signal such as a voltage or a current with respect to a specific waveform by a photo-detector may be represented by an Equation configured of an average value I′0 (or also called a 0 order Fourier coefficient) of the light intensity, Fourier coefficients A′D and B′D, a reference angular velocity ω, and N, which is a natural number indicating the highest order among normalized Fourier coefficient that is not 0, as in Equation 1:
                    [                  Equation          ⁢                                          ⁢          1                ]                                                                                  I            ex                    ⁡                      (            t            )                          =                              I            0            ′                    +                                    ∑                              D                =                1                            N                        ⁢                                          [                                                                            A                      D                      ′                                        ⁢                                          cos                      ⁡                                              (                                                  n                          ⁢                                                                                                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                              +                                                            B                      D                      ′                                        ⁢                                          sin                      ⁡                                              (                                                  n                          ⁢                                                                                                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                                            ]                            .                                                          (        1        )            
Since the components 21 of a Mueller-matrix for the sample 20 may be calculated from the Fourier coefficients I′0, A′D, and B′D, it is very important in the dual optical element rotation type ellipsometer to more accurately measure values of the Fourier coefficients from the waveform of the light intensity measured by the photo-detector as in Equation 1.
In measurement for components 21 of a 4×4 Mueller-matrix of the sample 20 using the rotating-polarizer rotating-analyzer ellipsometer according to the related art, in the case in which an angular velocity of the polarizer 13 rotating at a constant velocity in the polarization modifying unit 12 is set to ωP, an angular velocity of the analyzer 33 rotating at a constant velocity in the polarization analyzing unit 31 is set to ωA, and an angular velocity ratio between them is constantly maintained as in ωP·ωA=1:3, when a reference angular velocity in Equation 1 is determined to ω=ωP, a value of N becomes 8, such that a total of nine even number order Fourier coefficients may be measured. Therefore, as shown in FIG. 2, only nine components Mjj; i, j=1, 2, 3 among a total of sixteen components Mjj; i, j=1, 2, 3, 4 of the Mueller-matrix for the sample 20 are measurable values 21, and remaining seven components M14, M24, M34, M41, M42, M43, M44 are non-measurable values 22.
In measurement for components 21 of a 4×4 Mueller-matrix of the sample 20 using the rotating-compensator rotating-analyzer ellipsometer according to the related art, in the case in which an angular velocity of the first compensator 14 rotating at a constant velocity in the polarization modifying unit 12 is set to ωC1, an angular velocity of the analyzer 33 rotating at a constant velocity in the polarization analyzing unit 31 is set to ωA, and an angular velocity ratio between them is constantly maintained as in ωC1:ωA=3:1, when a reference angular velocity in Equation 1 is determined to ω=ωA, a value of N becomes 14, such that a total of fifteen even number order Fourier coefficients may be measured. Therefore, as shown in FIG. 3, only twelve components Mjj, i=1, 2, 3, j=1, 2, 3, 4 among a total of sixteen components Mjj; i, j=1, 2, 3, 4 of the Mueller-matrix for the sample 20 are measurable values 21, and remaining four components M41, M42, M43, M44 are non-measurable values 22.
In measurement for components 21 of a 4×4 Mueller-matrix of the sample 20 using the rotating-polarizer rotating-compensator ellipsometer according to the related art, in the case in which an angular velocity of the polarizer 13 rotating at a constant velocity in the polarization modifying unit 12 is set to ωP, an angular velocity of the second compensator 34 rotating at a constant velocity in the polarization analyzing unit 31 is set to ωC2, and an angular velocity ratio between them is constantly maintained as in ωC2:ωP=3:1, when a reference angular velocity in Equation 1 is determined to ω=ωP, a value of N becomes 14, such that a total of fifteen even number order Fourier coefficients may be measured. Therefore, as shown in FIG. 4, only twelve components Mjj; i=1,2,3,4, j=1, 2, 3 among a total of sixteen components Mjj; i, j=1, 2, 3, 4 of the Mueller-matrix for the sample 20 are measurable values 21, and remaining four components M14, M24, M34, M44 are non-measurable values 22.
In measurement for components 21 of a 4×4 Mueller-matrix of the sample 20 using the dual-rotating-compensator ellipsometer according to the related art, in the case in which an angular velocity of the first compensator 14 rotating at a constant velocity in the polarization modifying unit 12 is set to ωC1, an angular velocity of the second compensator 34 rotating at a constant velocity in the polarization analyzing unit 31 is set to ωC2, and an angular velocity ratio between them is constantly maintained as in ωC1:ωC2=1:5, when a reference angular velocity in Equation 1 is determined to ω=ωC1, a value of N becomes 24, such that a total of twenty five even number order Fourier coefficients may be measured. Therefore, from sixteen or more selected among measured values of a total of twenty five Fourier coefficients, as shown in FIG. 5, all of a total of sixteen components Mjj; i, j=1, 2, 3, 4 of the Mueller-matrix for the sample 20 are measurable values 21.
The dual optical element rotation type ellipsometers according to the related art except for the dual-rotating-compensator ellipsometer according to the related art have a problem that residual polarization of the light source and polarization dependence of the photo-detector cause an error of measurement. In order to completely solve this problem, both of the polarizer and the analyzer 33 should be in a stop state at a designated azimuth angle at the time of measurement.
In the case of a single polarizer rotation type ellipsometer and a single analyzer rotation type ellipsometer mainly used in single optical element rotation type ellipsometers according to the related art, the Fourier coefficients that are measured in Equation 1 and are not zero are (I′0, A′2, B′2), and in the case of a single compensator rotation type ellipsometer, the Fourier coefficients that are measured in Equation 1 and are not zero are (I′0, A′2, B′2, A′4, B′4). Therefore, the number of components of the Mueller-matrix to be measured is larger than that of measured values, such that it is impossible to calculate the components of the Mueller-matrix from the measured Fourier coefficients by a general method. On the other hand, in the dual optical element rotation type ellipsometers according to the related art capable of measuring some or all of the components of the Mueller-matrix, since a value of N is relatively larger as compared with the single optical element rotation type ellipsometers, Fourier coefficients of high frequency components by a change in an azimuth angle of an optical element rotating at a constant velocity in Equation 1 should be measured. Therefore, a measurement equation and a correction method are complicated. Particularly, in the case of the dual-rotating-compensator ellipsometer according to the related art capable of measuring all of the components of the Mueller-matrix, it has been generally well-known that since even Fourier coefficients of a high order term in Equation 1 should be measured, accuracy and precision in measuring the Fourier coefficients are relatively lower as compared with the single optical element rotation type ellipsometers. On the other hand, as a gradual miniaturization technology and a three-dimensionally complicated nano-structure are adopted in the nano-element manufacturing technology, a demand for gradual improvement of measurement accuracy and measurement precision in measuring shapes and physical properties of nano-patterns using the dual optical element rotation type ellipsometers according to the related art has increased in the nano-element industry fields.
Therefore, the development of Mueller-matrix ellipsometers capable of solving the above-mentioned problems has been demanded.